High-Dimensional Covariate-Dependent Gaussian Graphical Models

TL;DR

This paper introduces a covariate-dependent Gaussian graphical model that captures dynamic network structures varying with covariates, providing estimation, inference, and application to biological data.

Contribution

It proposes a novel parameterization for covariate-dependent networks and develops estimation and inference procedures for high-dimensional, dynamic biological networks.

Findings

Successfully models dynamic gene and protein networks

Establishes estimation error bounds and sign consistency

Demonstrates effectiveness on biological datasets

Abstract

Motivated by dynamic biologic network analysis, we propose a covariate-dependent Gaussian graphical model (cdexGGM) for capturing network structure that varies with covariates through a novel parameterization. Utilizing a likelihood framework, our methodology jointly estimates all dynamic edge and vertex parameters. We further develop statistical inference procedures to test the dynamic nature of the underlying network. Concerning large-scale networks, we perform composite likelihood estimation with an $\ell_1$ penalty to discover sparse dynamic network structures. We establish the estimation error bound in $\ell_2$ norm and validate the sign consistency in the high-dimensional context. We apply our method to an influenza vaccine data set to model the dynamic gene network that evolves with time. We also investigate a Down syndrome data set to model the dynamic protein network which varies under a factorial experimental design. These applications demonstrate the applicability and effectiveness of the proposed model. The supplemental materials for this article are available online.